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Snowpack Optical Properties in the Infrared BUREAU OF RECLAMATION LIBRARY REPORT 79-11 Snowpack optical properties in the infrared 70 s ~ <S> \ * *=> l,***»r AUb?8 1979 'ZSSSff* For conversion of SI metric units to U.S./British customary units of measurement consult ASTM Standard E380, Metric Practice Guide, published by the American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa. 19103. BUREAU OF RECLAMATION DENVER U6RARY 92028164 isoEfiim ■ ^ ^ l RREL Report 79-11 Oi Snowpack optical properties in the infrared Roger H. Berger May 1979 Prepared for DIRECTORATE OF MILITARY PROGRAMS OFFICE, CHIEF OF ENGINEERS By UNITED STATES ARMY CORPS OF ENGINEERS COLD REGIONS RESEARCH AND ENGINEERING LABORATORY HANOVER, NEW HAMPSHIRE, U.S.A. Approved for public release; distribution unlimited. Unclassified SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. R E P O R T N U M B E R 2. GOVT ACCESSION NO. 3. RECIPIENTS CATALOG-NUMBER ' -G R R E L 1 Report 79-11 4. T IT L E (and Subtitle) J 5. TYPE OF REPORT & PERIOD COVERED 3 SNOWPACK OPTICAL PROPERTIES IN THE INFRARED 6. PERFORMING ORG. REPORT NUMBER 7. AUTHOR!» 8. CONTRACT OR GRANT NUMBER!» Roger H. Berger s 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK A R E A & WORK UNIT NUMBERS U .S.% rny Cold Regions Research and Engineering Labefatury™ DA Project 4A762730AT42 Hanover, New Hampshire 03755 ^ Technical Area A1, Work Unit 004 11. CONTROLLING OFFICE NAME AND ADDRESS 12. R E P O R T D A T E Directorate of Military Programs ^ May 1979 Office, Chief of Engineers 13. N U M B E R O F P A G ES Washington, D.C. 20314 1 2 14. MONITORING AGENCY NAME & ADDRESS(7/ different from Controlling Office) 15. S E C U R IT Y CLASS, (of thia report) Unclassified 15a. DECL ASSI FI CATION/DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abatract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. K E Y WORDS (Continue on reverse aide if necesaary and identify by block number) Infrared radiation Optical properties Reflection Snow 2Qv ABSTRACT (C o n tìn u e en reverse atxtm ft naceaeary and. identity by block number) A theory of the optical properties of snow in the 2-20 jjtm region of the infrared has been developed. Using this theory it is possible to predict the absorption and scattering coefficients and the emissivity of snow, as a function of the snow parameters of grain size and density, for densities between 0.17 and 0.4 g/cm3. The absorption and scattering coefficients are linearly related to the density and inversely related to the average grain size. The emissivity is independent of grain size and exhibits only a weak dependence upon density. DD U73 EDITION OF t NOV 65 IS OBSOLETE Unclassified SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Entered) PREFACE This report was prepared by Roger H. Berger, Research Physicist, of the Physical Sciences Branch, Research Division, U.S. Army Cold Regions Research and Engineering Laboratory. Funding for this project was provided by DA Project 4A762730AT42, Design, Construction and Operations Technoiogy for Cold Regions, Technical area A1, ice and Snow Technology, Work Unit 004, Camouflage and Decoy Techniques in Winter Environments. The author gratefully acknowledges the interest and suggestions of Dr. Y.C. Yen and Dr. S.C. Colbeck, who technically reviewed the manuscript of this report. ii NOMENCLATURE a particle radius C single particle cross section E energy f fraction of the snowpack surface occupied by ice particles H irradiance K absorption coefficient N number of particles/unit volume n refractive index Q factor used to convert the transmission coefficient to the transmissivity and assure the con­ servation of radiant energy at an interface R reflectivity T transmissivity X extinction coefficient 7 radiation phase change produced by transmission across a boundary e emissivity r \ radiation phase change produced by reflection at a boundary 0 angle of incidence or coaltitude X wavelength p density a scattering coefficient f skin depth <t> angle of refraction azimuth angle Subscripts c cavity, denotes the emissivity associated with the pores on the snowpack surface i ice, incident and imaginary used as p }, 0j and /7j, respectively r real s snow, denotes properties associated with the bulk snowpack ab absorption ext extinction sc scattering tr transmitted iii SNOWPACK OPTICAL PROPERTIES IN THE INFRARED Roger H. Berger INTRODUCTION and transmission coefficients and the emissivity of a snowpack from its mean grain size and density. The interaction of electromagnetic radiation with a As shown in Figure 1, the infrared region of the natural snow cover is of considerable practical interest electromagnetic spectrum extends from about 0.8 to and scientific importance. The remote sensing com­ 1000 jum, but absorption by yarious atmospheric con­ munity requires an improved understanding of the op­ stituents limits most infrared remote sensing to two tical properties of snow in order to correctly interpret atmospheric windows at 3-5 and 8-14 /jm. The theory the imagery of snow-covered regions and to distinguish of the infrared optical properties of snow developed in between snowpacks and cloud covers. Radiant energy this report is valid for wavelengths between 2 and 20 transfer is important in the thermodynamics and meta­ pm, the region most useful for remote sensing. morphosis of the snowpack and is therefore of inter­ est to those who study the mechanical and hydrologi­ cal properties of the snowpack. Therefore, the estab­ THE MODEL lishment o f relationships between the optical proper­ ties o f snow and frequently measured snowpack Radiation incident upon the snowpack surface under­ quantities, such as grain size and density, would be of goes either single or multiple interactions as illustrated considerable utility. A model is proposed in this re­ in Figure 2. These multiple interactions have been port for estimating the infrared absorption, reflection treated by Dunkle and Gler (1955) and Bergen (1970) o Visible A /J. m cm m -----------------IO11----- IO2 IO3 IO0 IO1 IO2 IOH IO0 IO1 10° a. The electromagnetic spectrum. ----- r ------- --------1 mr * r~ " i '1 t er S 1— Î " '2 I I1 'U H F1 v h f X-Rays uv P ; I R ■ Radio * Expanded Area b. Designations within the infrared region o f the electromagnetic spectrum. c. A tmospheric transmission in the infrared showing the principal atmos­ pheric constituents causing absorp­ tion. The horizontal arrows indi­ cate the atmospheric "windows” through which most remote sensing in the infrared is done. Figure 7. The electromagnetic spectrum. Incident applicable to this model two conditions have to be satisfied. First, the particles must be large compared to the wavelength of the radiation. Second, the inter­ granular spacing must be large compared to the average grain dimensions. The first condition is easily satisfied, since for most snows, the mean grain diameter is more than an order of magnitude larger than 20 pm, the maximum wavelength considered here. The second implies that the geometrical optics approach is valid only for low-density snow. The range of snow densities for which this assumption is valid will be examined more closely in relation to the results of the theory. RADIANT INTERACTIONS If we consider a single grain within the snowpack, it emits radiation isotropically and is immersed in the flux of radiation from the surrounding grains. Let us con­ sider this external radiation flux as a plane wave and examine the interaction between it and an ice particle. Figure 2. Interaction between electromagnetic radia­ This incident radiation of intensity H will either be tion and the surface layer o f ice particles in a snow- absorbed or scattered and these processes can be des­ pack. The solid lines represent the incident radiation , cribed in terms of the single particle cross sections Cab the dotted lines represent radiation that is specularly for absorption and for scattering. These cross sec­ reflected either singly or m ultiply , and the bold dashed tions are defined by the ratios of the energy absorbed lines represent refracted and absorbed radiation. or scattered to the incident flux: and Giddings and LaChapelle (1961) as a radiative Cab s f ° r absorption (1a) transfer or diffusion problem in a continuum. If the work of these authors is extended from the visible to and infrared wavelengths, problems arise due to the large absorption coefficient of ice in the infrared. Csc = F sc/H for scattering. (1b) A much simpler approach to this scattering prob­ lem and one which is easily adaptable to the longer in­ By the law of conservation of energy these cross sections frared wavelengths is to look at the problem in terms are related to the extinction cross section: of geometrical optics (Bohren and Barkstrom 1974). A rigorous treatment of the snowpack model proposed ^ext ^ab+^sc* (2) in this report would require Mie scattering theory, but the arbitrary shapes of the actual ice grains within the With the initial assumption of a random distribution of snowpack make this refinement unnecessary. grains spaced relatively far apart, these cross sections may be related to the bulk material absorption, scatter­ ing and extinction coefficients by SNOWPACK DESCRIPTION *s = C*N (3a) The snowpack model proposed is a random distri­ bution of spherical ice grains immersed in a nonabsorb­ o , = C scN (3b) ing medium. Below the plane which defines the sur­ face of the snowpack, the grain distribution is homo­ X s = C eMN . (3c) geneous and isotropic and may be characterized by the mean grain radius a, the density of ice pj and the The assumptions of large grain separation and random snow density p s.
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